OFFSET
1,4
COMMENTS
The asymptotic mean of this sequence is 1 (Niven, 1969). -Amiram Eldar,Jul 10 2020
Let k =A007947(n), then for n > 1 k^a(n) is the greatest power of k which divides n; see example. -David James Sycamore,Sep 07 2023
LINKS
Daniel Forgues,Table of n, a(n) for n = 1..100000
Cao Hui-Zhong,The Asymptotic Formulas Related to Exponents in Factoring Integers,Math. Balkanica, Vol. 5 (1991), Fasc. 2.
Ivan Niven,Averages of Exponents in Factoring Integers,Proc. Amer. Math. Soc., Vol. 22, No. 2 (1969), pp. 356-360.
Eric Weisstein's World of Mathematics,Niven's Constant
FORMULA
EXAMPLE
For n = 72 = 2^3*3^2, a(72) = min(exponents) = min(3,2) = 2.
For n = 72, using alternative definition: rad(72) = 6; and 6^2 = 36 divides 72 but no higher power of 6 divides 72, so a(72) = 2.
For n = 432, rad(432) = 6 and 6^3 = 216 divides 432 but no higher power of 6 divides 432, therefore a(432) = 3. -David James Sycamore,Sep 08 2023
MAPLE
a:= proc (n) if n = 1 then 0 else min(seq(op(2, op(j, op(2, ifactors(n)))), j = 1.. nops(op(2, ifactors(n))))) end if end proc: seq(a(n), n = 1.. 100); #Emeric Deutsch,May 20 2015
MATHEMATICA
Table[If[n == 1, 0, Min @@ Last /@ FactorInteger[n]], {n, 100}] (*Ray Chandler,Jan 24 2006 *)
PROG
(Haskell)
a051904 1 = 0
a051904 n = minimum $ a124010_row n --Reinhard Zumkeller,Jul 15 2012
(PARI) a(n)=vecmin(factor(n)[, 2]) \\Charles R Greathouse IV,Nov 19 2012
(Scheme) (define (A051904n) (cond ((= 1 n) 0) ((= 1 (A001221n)) (A001222n)) (else (min (A067029n) (A051904(A028234n))))));;Antti Karttunen,Jul 12 2017
(Python)
from sympy import factorint
def a(n):
f = factorint(n)
l = [f[p] for p in f]
return 0 if n == 1 else min(l)
print([a(n) for n in range(1, 51)]) #Indranil Ghosh,Jul 13 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer,Dec 16 1999
STATUS
approved